Even before they play a note, the mere sight on the Royal Albert Hall platform of the orchestra Daniel Barenboim and Edward Said co-founded 16 years ago, consisting almost entirely of young musicians from Israel and the Arab countries, remains a uniquely inspiring one.

They began their Prom with Schoenberg’s First Chamber Symphony, a relatively early piece from 1906. Like all of Schoenberg’s music, the result is thematically dense, even though its textures are as open and airy as one would expect from 15 solo players assembled in a large chamber grouping, rather than a slimmed-down orchestral ensemble. Individual playing standards were consistently high, though there were a few untidy moments, and the piece needed a keener sense of momentum to maximise its expressive coherence.

Next, Barenboim took to the piano both to direct and play one of the solo parts in Beethoven’s Triple Concerto, alongside the Israeli violinist Guy Braunstein and the Persian cellist Kian Soltani. This might have been one time when handing over either the baton or the keyboard would have benefited the work itself, which could have done with more consistent impetus. In terms of tone and technique, the charismatic Soltani had the advantage over his violinist colleague.

It was after the interval that the concert really rose to the heights, lifting into the air with the minatory fanfares that open Tchaikovsky’s Fourth Symphony, and staying there for the duration of the emotionally charged piece. Lightly directed by Barenboim, the orchestra rose to all technical challenges in an interpretation of overwhelming energy and power. By the time they reached encores by Sibelius, Glinka and José Carli, they were firing on all cylinders.

• On iPlayer from 21 August for 30 days. The Proms continue until 12 September.